The Agnatha as a whole may be paraphyletic.[1] This means it is a convenient holdall term, which does not follow the rules of cladistics. For example, most extinct agnathans belong to the stem group (ancestral group) of gnathostomes.[2][3] But according to the rules, one sister group should not contain ancestors of another sister group,

Many Ordovician, Silurian, and Devonian agnathans were armoured with heavy bony-spiky plates. The first armoured agnathans were the Ostracoderms ("shell-skinned").[8] By the upper Silurian the agnathans had reached the high point of their evolution. They declined in the Devonian and never recovered.